prior_predictive_check

library load

library(tidyverse)
library(glue)
library(tidybayes)
library(cowplot)
library(scales)
library(GGally)
library(knitr)
library(matrixStats)

theme_set(theme_cowplot())

load_existing_sim <- TRUE

I’m starting this prior check with the work I’ve already done in the sandbox. In those scripts I already got a sense of what weakly informative priors for my starting model might be. In those files, I only did a visual inspection of the prior predictive distribution, not neccesarily including any summary statistics. I also did not do any sort of checks based on the sample size of the small design I have.

model

Written down the model is:

\[ \begin{aligned} \mathrm{-likelihood-} \\ error_i &\sim (pMem_i)*VM(0, \kappa_i) + (1 - pMem_i)*Unif(-\pi,\pi) \\ \\ \mathrm{-param~transformation-} \\ \kappa_i &= sd2k(circ\_sd_i) \\ \\ \mathrm{-linear~model-} \\ circ\_sd_i &= exp(\alpha_{0,SUBJ[i]} + \alpha_{\Delta,SUBJ[i]} * postCond) ~~ \mathrm{-log~link~on~sd-} \\ pMem_i &= inv\_logit(\beta_{0,SUBJ[i]} + \beta_{\Delta,SUBJ[i]} * postCond) ~~ \mathrm{-logit~link~on~pMem-} \\ \\ \mathrm{-priors:~all~independent-}\\ \alpha_{0,SUBJ[...]} &\sim Normal(mu\_\alpha_0, sigma\_\alpha_0) \\ \alpha_{\Delta,SUBJ[...]} &\sim Normal(mu\_\alpha_{\Delta}, sigma\_\alpha_{\Delta}) \\ \beta_{0,SUBJ[...]} &\sim Normal(mu\_\beta_0, sigma\_\beta_0) \\ \beta_{\Delta,SUBJ[...]} &\sim Normal(mu\_\beta_{\Delta}, sigma\_\beta_{\Delta}) \\ \\ mu\_\alpha_0 &\sim Normal(4, 0.5)\\ sigma\_\alpha_0 &\sim Normal^+(0, 0.5) \\ mu\_\alpha_{\Delta} &\sim Normal(0, 0.5)\\ sigma\_\alpha_{\Delta} &\sim Normal^+(0, 0.5)\\ mu\_\beta_0 &\sim Normal(0, 1.5)\\ sigma\_\beta_0 &\sim Normal^+(0, 1.5)\\ mu\_\beta_{\Delta} &\sim Normal(0, 1)\\ sigma\_\beta_{\Delta} &\sim Normal^+(0, 1)\\ \end{aligned} \]

---

real obs load

I am considering the color stimulation data. samples sizes:

obs_data <- read_csv(glue('{params$model_dir_str}/data/stimulation_obvs.csv'))

## Parsed with column specification:
## cols(
##   subj = col_double(),
##   subj_index = col_double(),
##   stimulation = col_double(),
##   error = col_double()
## )

#summarize subj num, obs count, and obs condition split
(subj_summary <- obs_data %>%
  group_by(subj_index) %>%
  summarise(n_obs = n(), frac_stim = mean(stimulation)))

## # A tibble: 2 x 3
##   subj_index n_obs frac_stim
##        <dbl> <int>     <dbl>
## 1          1   252       0.5
## 2          2   252       0.5

2 subjs with 252 observations each, 126 per condition.

9/12 - I am thinking I should simulate varying effects using the actual samples sizes I have. I also think that this shouldnt matter (at least for a model like this). I’ll also try with a larger number of subjects.

---

Simulation

nsubj_sim <- 15
nobs_per_cond_sim <- 1500

functions

source(glue("{params$common_dir_str}/simulation.R"))

run simulate

source(glue("{params$model_dir_str}/model_prior.R"))

print(bprior_full)

##            prior class        coef group resp   dpar nlpar bound
## 1 normal(4, 0.5)     b   intercept            circSD            
## 2 normal(0, 0.5)     b stimulation            circSD            
## 3 normal(0, 0.5)    sd   Intercept  subj      circSD            
## 4 normal(0, 0.5)    sd stimulation  subj      circSD            
## 5 normal(0, 1.5)     b   intercept             theta            
## 6   normal(0, 1)     b stimulation             theta            
## 7 normal(0, 1.5)    sd   Intercept  subj       theta            
## 8   normal(0, 1)    sd stimulation  subj       theta

conditions <- c(0,1)

sim_datasets_fpath <- glue("{params$save_dir_str}/sim_datasets.rds")

found_existing_sim <- FALSE
if (file.exists(sim_datasets_fpath)){
  found_existing_sim <- TRUE
}


if (load_existing_sim == FALSE || found_existing_sim == FALSE){

  print("simulating")
  
  nsim_datasets <- 2000
  
  sim_priors <- tibble(
    sim_num = 1:nsim_datasets,
    alpha0_mu = rnorm(nsim_datasets, alpha0_mu_prior_mu, alpha0_mu_prior_sd),
    alpha0_sigma = abs(rnorm(nsim_datasets, alpha0_sigma_prior_mu, alpha0_sigma_prior_sd)),
    alphaD_mu =  rnorm(nsim_datasets, alphaD_mu_prior_mu, alphaD_mu_prior_sd),
    alphaD_sigma = abs(rnorm(nsim_datasets, alphaD_sigma_prior_mu, alphaD_sigma_prior_sd)),
    beta0_mu = rnorm(nsim_datasets, beta0_mu_prior_mu, beta0_mu_prior_sd),
    beta0_sigma = abs(rnorm(nsim_datasets, beta0_sigma_prior_mu, beta0_sigma_prior_sd)),
    betaD_mu = rnorm(nsim_datasets, betaD_mu_prior_mu, betaD_mu_prior_sd),
    betaD_sigma = abs(rnorm(nsim_datasets, betaD_sigma_prior_mu, betaD_sigma_prior_sd)),
    nsubj = nsubj_sim,
    nobs_per_cond = nobs_per_cond_sim
  )
  
  sim_datasets <- 
    sim_priors %>%
    mutate(
      # use draw_subj to sample nsubj_sim per sim using group-level parameter draws
      dataset = pmap(sim_priors, draw_subj),
      stimulation = list(stimulation = rep(conditions, each = nobs_per_cond_sim))) %>%
    
    # first unnest dataset, expanding by nsubj_sim and copying stimulation list to each subj
    unnest(dataset) %>%
    
    # then unnest stimulation, expanding by nobs_per_cond_sim*2
    unnest(stimulation) %>%
    
    # now use likelihood to simulation observations
    mutate(
      # evaluate and delink linear model on pMem
      pMem = inv_logit(subj_beta0 + (subj_betaD * stimulation)),
      
      # evaluate and delink linear model on circSD/kappa
      k = sd2k_vec(
        pracma::deg2rad(
          exp(subj_alpha0 + (subj_alphaD * stimulation)))),
      
      # use pMem to draw a 1 or 0 for each trial
      memFlip = rbernoulli(n(), pMem),
      
      # use k to draw from vonMises for each trial
      vm_draw = rvonmises_vec(1, pi, k) - pi,
      
      # draw from unif for each trial
      unif_draw = runif(n(), -pi, pi),
      
      # assign either vm_draw or unif_draw to each trial, depending on memFlip
      obs_radian = memFlip * vm_draw + (1 - memFlip) * unif_draw,
      
      # convert to degrees
      obs_degree = obs_radian * (180/pi)
    ) %>%
    select(-c(pMem, k, memFlip, vm_draw, unif_draw)) %>%
    nest(subj_obs = c(stimulation, obs_degree, obs_radian)) %>%
    nest(dataset = c(subj, subj_alpha0, subj_alphaD, subj_beta0, subj_betaD, nobs_per_condition, subj_obs))

  
  saveRDS(sim_datasets, file = sim_datasets_fpath)

}else{
  
  sim_datasets <- readRDS(sim_datasets_fpath)
}

Check sim data

head(sim_datasets)

## # A tibble: 6 x 12
##   sim_num alpha0_mu alpha0_sigma alphaD_mu alphaD_sigma beta0_mu
##     <int>     <dbl>        <dbl>     <dbl>        <dbl>    <dbl>
## 1       1      4.72       0.951     0.386        0.644    -3.04 
## 2       2      3.85       0.271     0.602        0.210     3.63 
## 3       3      3.82       0.629     0.574        0.0698    0.648
## 4       4      3.37       0.0409    0.503        0.0315   -0.111
## 5       5      4.07       1.13     -1.15         0.447    -1.91 
## 6       6      4.39       0.298    -0.0236       0.590    -0.470
## # … with 6 more variables: beta0_sigma <dbl>, betaD_mu <dbl>,
## #   betaD_sigma <dbl>, nsubj <dbl>, nobs_per_cond <dbl>, dataset <S3:
## #   vctrs_list_of>

head(sim_datasets$dataset[[1]])

## # A tibble: 6 x 7
##    subj subj_alpha0 subj_alphaD subj_beta0 subj_betaD nobs_per_condit…
##   <int>       <dbl>       <dbl>      <dbl>      <dbl>            <dbl>
## 1     1        4.25      0.304       -2.68    -0.673              1500
## 2     2        5.07      0.0856      -2.80     0.195              1500
## 3     3        5.03      1.45        -2.82    -0.474              1500
## 4     4        4.96      0.823       -3.02    -0.0157             1500
## 5     5        3.35     -0.295       -3.30    -0.636              1500
## 6     6        2.54     -0.0165      -3.09    -1.08               1500
## # … with 1 more variable: subj_obs <S3: vctrs_list_of>

head(sim_datasets$dataset[[1]]$subj_obs[[1]])

## # A tibble: 6 x 3
##   stimulation obs_degree obs_radian
##         <dbl>      <dbl>      <dbl>
## 1           0      172.       3.00 
## 2           0       25.2      0.439
## 3           0       94.8      1.65 
## 4           0      133.       2.33 
## 5           0      111.       1.94 
## 6           0       62.6      1.09

---

Plot distributions and summary statistics

Ideas:

Definitely plot the priors on the intercept and slope means, transformed back into sd

plot the prior predicitive densities for subjects

Some other plot ideas:

shaded histogram plot, combining data across stimulation conditions - check if data looks too peaked or too flat

shaded histogram plot, one for each stimulation condition - same check ^

plot of density lines, one from each sim dataset, one with both conditions and one with them split out - this would help identify weird distribution more that shaded histogram perhaps

Correctness checks that prior samples are drawn correctly

sim_datasets %>%
  select(alpha0_mu, alpha0_sigma, alphaD_mu, alphaD_sigma) %>%
  ggpairs(progress = FALSE)

sim_datasets %>%
  select(beta0_mu, beta0_sigma, betaD_mu, betaD_sigma) %>%
  ggpairs(progress = FALSE)

Correctness check of likelihood simulation

param_set <- cross_df(list(pMem = seq(0, 1, 0.1), sd = seq(20, 50, 5)))

param_set %>%
  mutate(sims = map2(param_set$pMem, sd2k_vec(pracma::deg2rad(param_set$sd)), ~simulateData_likelihood(.x, .y, 1000))) %>%
  unnest(sims) %>% 
  ggplot(aes(x = obs_degree)) + 
  geom_histogram(binwidth = 1) +
  facet_grid(rows = vars(pMem), cols = vars(sd), labeller = 'label_both', scales = 'free')

param_set <- cross_df(list(pMem = seq(0, 1, 0.1), sd = seq(55, 105, 5)))

param_set %>%
  mutate(sims = map2(param_set$pMem, sd2k_vec(pracma::deg2rad(param_set$sd)), ~simulateData_likelihood(.x, .y, 1000))) %>%
  unnest(sims) %>% 
  ggplot(aes(x = obs_degree)) + 
  geom_histogram(binwidth = 1)+
  facet_grid(rows = vars(pMem), cols = vars(sd), labeller = 'label_both')

* Notes

all good here.

---

Prior distribution on von-mises circSD, linear model parameters

(pre group mean, post group mean, post-pre mean change)

No accounting for subject variance here

##
## alpha0_mu 
##

## linked prior distribution
alpha0_mu_hist <- sim_datasets %>%
  ggplot(aes(x = alpha0_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#F16C66") +
  theme(legend.position = "none",
        axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  labs(x = "linked prior on group mean for circSD, pre condition",
       title = "circSD group mean prior, alpha0_mu") + 
  scale_x_continuous(limits = c(1,7))
  

##
## alpha0_mu + alphaD_mu = alpha1_mu 
##

## linked prior distribution
alpha1_mu_hist <- sim_datasets %>%
  transmute(alpha1_mu = alpha0_mu + alphaD_mu) %>%
  ggplot(aes(x = alpha1_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#685369") +
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) +
  labs(x = "linked prior on group mean for circSD, post condition",
       title = "circSD group mean prior, alpha0_mu + alphaD_mu") + 
  scale_x_continuous(limits = c(1,7))


plot_grid(alpha0_mu_hist, alpha1_mu_hist, nrow = 1, align = "h")

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

##
## alpha0_mu 
##

## delinked prior alpha0_mu
alpha0_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu)) %>%
  summarise(less_than_5 = sum(delinked < 5)/n(), greater_than_120 = sum(delinked > 120)/n())

alpha0_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu)) %>%
  ggplot(aes(x = delinked)) +
  geom_histogram(binwidth = 2, fill = "#F16C66") + 
  geom_vline(xintercept = c(5, 120), linetype = "dashed") + 
  labs(x = "prior on group mean for circSD, pre condition",
       title = "circSD group mean prior, exp(alpha0_mu)",
       subtitle = glue("prob(circSD < 5) = {alpha0_mu_delinked_stats$less_than_5}\nprob(circSD > 120) = {alpha0_mu_delinked_stats$greater_than_120}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) 
  
##
## alpha0_mu + alphaD_mu = alpha1_mu 
##  
  
## delinked prior alpha0_mu + alphaD_mu
alpha1_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 2, fill = "#685369") + 
  labs(x = "prior on group mean for circSD, post condition",
       title = "circSD group mean prior, exp(alpha0_mu + alphaD_mu)") + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))


plot_grid(alpha0_mu_delinked_hist, alpha1_mu_delinked_hist, nrow = 1, align = "h")

##
## exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu) plot
##

alphaD_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)) %>%
  summarise(less_than_n100 = sum(delinked < -100)/n(), greater_than_100 = sum(delinked > 100)/n())

alphaD_mu_delinked_hist <- sim_datasets %>%
  transmute(delinked = exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 2, fill = "#00AEB2") + 
  geom_vline(xintercept = c(-100, 100), linetype = "dashed") + 
  labs(x = "prior on group mean for delta-circSD, mean post minus mean pre",
       title = "delta-circSD group mean prior, exp(alpha0_mu + alphaD_mu) - exp(alpha0_mu)",
       subtitle = glue("prob(delta-circSD < -100) = {alphaD_mu_delinked_stats$less_than_n100}\nprob(delta-circSD > 100) = {alphaD_mu_delinked_stats$greater_than_100}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  scale_x_continuous(breaks= pretty_breaks(10))

alphaD_mu_delinked_hist

* Notes

circSD group mean prior (pre + post) - too wide, too much probability stretching past 100 circSD group mean ES - all wider than need be

---

Prior predicitive distribution on circSD at the subject level

(based on simulated subjects from each dataset)

These plots indicate the effects of the priors on alpha0_mu, alpha0_sigma, alphaD_mu, alphaD_sigma.

Marginal prior on subjects pre circSD, post circSD, and effect size

(ignoring simulation sample sizes)

sim_datasets_unnest <- sim_datasets %>%
  unnest(dataset) %>%
  mutate(alpha0_mu_delinked = exp(alpha0_mu),
         alpha1_mu_delinked = exp(alpha0_mu + alphaD_mu),
         subj_pre_circSD = exp(subj_alpha0),
         subj_post_circSD = exp(subj_alphaD + subj_alpha0),
         subj_circSD_ES = subj_post_circSD - subj_pre_circSD) 

subj_pre_circSD_plot <- sim_datasets_unnest %>%
  mutate(subj_pre_circSD = if_else(subj_pre_circSD > 120, 120, subj_pre_circSD)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_pre_circSD)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.3) + 
  labs(x = "subj_pre_circSD [prior predictive distribution]",
       subtitle = glue("p(<5) = {sum(sim_datasets_unnest$subj_pre_circSD < 5)/length(sim_datasets_unnest$subj_pre_circSD)}\n p(>120) = {sum(sim_datasets_unnest$subj_pre_circSD > 120)/length(sim_datasets_unnest$subj_pre_circSD)}"))


subj_post_circSD_plot <- sim_datasets_unnest %>%
  mutate(subj_post_circSD = if_else(subj_post_circSD > 120, 120, subj_post_circSD)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_post_circSD)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.3) + 
  labs(x = "subj_post_circSD [prior predictive distribution]",
       subtitle = glue("p(<5) = {sum(sim_datasets_unnest$subj_post_circSD < 5)/length(sim_datasets_unnest$subj_post_circSD)}\n p(>120) = {sum(sim_datasets_unnest$subj_post_circSD > 120)/length(sim_datasets_unnest$subj_post_circSD)}"))


subj_circSD_ES_plot <- sim_datasets_unnest %>%
  mutate(subj_circSD_ES = if_else(subj_circSD_ES > 100, 100, subj_circSD_ES)) %>%
  mutate(subj_circSD_ES = if_else(subj_circSD_ES < -100, -100, subj_circSD_ES)) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_circSD_ES)) + 
  geom_histogram(binwidth = 5, fill = "red", alpha = 0.7) + 
  labs(x = "subj_circSD_ES [prior predictive distribution]",
       subtitle = glue("p(< -100) = {sum(sim_datasets_unnest$subj_circSD_ES < -100)/length(sim_datasets_unnest$subj_circSD_ES)}\n p(>100) = {sum(sim_datasets_unnest$subj_circSD_ES > 100)/length(sim_datasets_unnest$subj_circSD_ES)}"))

plot_grid(subj_pre_circSD_plot, subj_post_circSD_plot, subj_circSD_ES_plot, ncol = 1)

Calculate min and max subject pre, post, and circSD effect size in each simulation.

sim_subj_extremes <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_alpha1 = subj_alpha0 + subj_alphaD, 
         subj_alpha0_delinked = exp(subj_alpha0), 
         subj_alpha1_delinked = exp(subj_alpha1), 
         subj_circSD_effect = subj_alpha1_delinked - subj_alpha0_delinked ) %>%
  group_by(sim_num) %>%
  summarize_at(vars(subj_alpha0_delinked, subj_alpha1_delinked, subj_circSD_effect), list(max = max, min = min)) 

Across-sim SD of circSD

simSD <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_pre_circSD = exp(subj_alpha0),
         subj_post_circSD = exp(subj_alpha0 + subj_alphaD)) %>%
  group_by(sim_num) %>%
  summarise_at(vars(subj_pre_circSD, subj_post_circSD), list(mean = mean, sd = sd))

plot_grid(
  
  ggplot(simSD, aes(subj_pre_circSD_sd)) + 
    geom_histogram(binwidth = 2) + 
    xlim(0, 200) + 
    labs(x = "pre condition: observed SD of distribution of circSD, per sim", 
         subtitle = glue::glue("p(>50) = {mean(simSD$subj_pre_circSD_sd > 50)}")),
  
  ggplot(simSD, aes(subj_post_circSD_sd)) + 
    geom_histogram(binwidth = 2) +
    xlim(0, 200) + 
    labs(x = "post condition: observed SD of distribution of circSD, per sim",
        subtitle = glue::glue("p(>50) = {mean(simSD$subj_post_circSD_sd > 50)}")),
  
  ncol = 1
  )                                                             

## Warning: Removed 28 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 137 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

plot_grid(
  
  ggplot(simSD, aes(subj_pre_circSD_mean, subj_pre_circSD_sd)) + 
    geom_point() + 
    xlim(0, 200) + ylim(0, 100) + 
    labs(x = "pre condition: observed mean of distribution of circSD, per sim",
         y = "pre condition: observed sd"),
  
  ggplot(simSD, aes(subj_post_circSD_mean, subj_post_circSD_sd)) + 
    geom_point() +
    xlim(0, 200) + ylim(0, 100) + 
    labs(x = "post condition: observed mean of distribution of circSD, per sim",
         y = "post condition: observed sd"),
  
  ncol = 1
  )                                                             

## Warning: Removed 127 rows containing missing values (geom_point).

## Warning: Removed 373 rows containing missing values (geom_point).

Across-sim max circSD

#What is the max subject pre condition value in each dataset
pre_plot <- sim_subj_extremes %>%
  mutate(subj_alpha0_delinked_max = if_else(subj_alpha0_delinked_max > 120, 120, subj_alpha0_delinked_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha0_delinked_max, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: max subj circSD per sim [subj_alpha0_delinked_max]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha0_delinked_max < 5)/length(sim_subj_extremes$subj_alpha0_delinked_max)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha0_delinked_max > 120)/length(sim_subj_extremes$subj_alpha0_delinked_max)}"))

#What is the max subject post condition value in each dataset
post_plot <- sim_subj_extremes %>%
  mutate(subj_alpha1_delinked_max = if_else(subj_alpha1_delinked_max > 120, 120, subj_alpha1_delinked_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha1_delinked_max, fill = "red", alpha = 0.3), binwidth = 5) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: max subj circSD per sim [subj_alpha1_delinked_max]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha1_delinked_max < 5)/length(sim_subj_extremes$subj_alpha1_delinked_max)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha1_delinked_max > 120)/length(sim_subj_extremes$subj_alpha1_delinked_max)}"))


plot_grid(pre_plot, post_plot, ncol =1, align = 'v')

Across-sim min circSD

pre_plot <- sim_subj_extremes %>%
  mutate(subj_alpha0_delinked_min = if_else(subj_alpha0_delinked_min > 120, 120, subj_alpha0_delinked_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha0_delinked_min, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: min subj circSD per sim [subj_alpha0_delinked_min]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha0_delinked_min < 5)/length(sim_subj_extremes$subj_alpha0_delinked_min)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha0_delinked_min > 120)/length(sim_subj_extremes$subj_alpha0_delinked_min)}"))

#What is the most extreme subject post condition value in each dataset
post_plot <- sim_subj_extremes %>%
  mutate(subj_alpha1_delinked_min = if_else(subj_alpha1_delinked_min > 120, 120, subj_alpha1_delinked_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_alpha1_delinked_min, fill = "red", alpha = 0.3), binwidth = 5) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: min subj circSD per sim [subj_alpha1_delinked_min]",
       subtitle = glue("p(<5) = {sum(sim_subj_extremes$subj_alpha1_delinked_min < 5)/length(sim_subj_extremes$subj_alpha1_delinked_min)}\n p(>120) = {sum(sim_subj_extremes$subj_alpha1_delinked_min > 120)/length(sim_subj_extremes$subj_alpha1_delinked_min)}"))


plot_grid(pre_plot, post_plot, ncol =1, align = 'v')

Across-sim max+min circSD effect size

#What is the most extreme change from pre to post in a subject

min_plot <- sim_subj_extremes %>%
  mutate(subj_circSD_effect_min = if_else(subj_circSD_effect_min > 100 , 100, subj_circSD_effect_min)) %>%
  mutate(subj_circSD_effect_min = if_else(subj_circSD_effect_min < -100 , -100, subj_circSD_effect_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_circSD_effect_min, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "min subj circSD effect per sim \n[min(subj_alpha1_delinked - subj_alpha0_delinked)]",
       subtitle = glue("p(<-100) = {sum(sim_subj_extremes$subj_circSD_effect_min < -100)/length(sim_subj_extremes$subj_circSD_effect_min)}\n p(>100) = {sum(sim_subj_extremes$subj_circSD_effect_min > 100)/length(sim_subj_extremes$subj_circSD_effect_min)}"))

#What is the most extreme subject post condition value in each dataset
max_plot <- sim_subj_extremes %>%
  mutate(subj_circSD_effect_max = if_else(subj_circSD_effect_max > 100 , 100, subj_circSD_effect_max)) %>%
  mutate(subj_circSD_effect_max = if_else(subj_circSD_effect_max < -100 , -100, subj_circSD_effect_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_circSD_effect_max, fill = "red", alpha = 0.3), binwidth = 5) +
  theme(legend.position = "none") + 
  labs(x = "max subj circSD effect per sim \n[max(subj_alpha1_delinked - subj_alpha0_delinked)]",
       subtitle = glue("p(<-100) = {sum(sim_subj_extremes$subj_circSD_effect_max < -100)/length(sim_subj_extremes$subj_circSD_effect_max)}\n p(>100) = {sum(sim_subj_extremes$subj_circSD_effect_max > 100)/length(sim_subj_extremes$subj_circSD_effect_max)}"))

plot_grid(min_plot, max_plot, ncol =1, align = 'v')

* Notes

way too much probability given to seeing subjects with extreme circSD and extreme ES

measured SD of subjects circSD is also way too large

the same is true of max and min circSD, ES across sim subjects

---

Prior distribution on mixture probability pMem, linear model parameters

(pre group mean, post group mean, post-pre mean change)

## linked prior distribution


plot_grid(
  
  sim_datasets %>%
  ggplot(aes(x = beta0_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#F16C66") +
  theme(legend.position = "none",
        axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  labs(x = "linked prior on group mean for pMem, pre condition",
       title = "pMem group mean prior, beta0_mu") + 
  scale_x_continuous(limits = c(-5,5))
  
  ,
  
  sim_datasets %>%
  transmute(beta1_mu = beta0_mu + betaD_mu) %>%
  ggplot(aes(x = beta1_mu)) + 
  geom_histogram(binwidth = 0.05, fill = "#685369") +
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) +
  labs(x = "linked prior on group mean for pMem, post condition",
       title = "pMem group mean prior, beta0_mu + betaD_mu") + 
  scale_x_continuous(limits = c(-5,5))
  
  ,
  
  nrow = 1,
  align = "h"
)

## Warning: Removed 1 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 9 rows containing non-finite values (stat_bin).

## Warning: Removed 2 rows containing missing values (geom_bar).

##
## inv_logit(beta0_mu)
##

##
## inv_logit(beta0_mu + betaD_mu) = inv_logit(beta1_mu) 
##  

## delinked prior alpha0_mu
beta0_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  summarise(less_than_5 = sum(delinked < 0.05)/n(), greater_than_95 = sum(delinked > 0.95)/n())

plot_grid(
  
  sim_datasets %>%
  transmute(delinked = exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  ggplot(aes(x = delinked)) +
  geom_histogram(binwidth = 0.03, fill = "#F16C66") + 
  geom_vline(xintercept = c(0.05, 0.95), linetype = "dashed") + 
  labs(x = "prior on group mean for pMem, pre condition",
       title = "pMem group mean prior, inv_logit(beta0_mu)",
       subtitle = glue("prob(pMem < 0.05) = {beta0_mu_delinked_stats$less_than_5}\nprob(pMem > 0.95) = {beta0_mu_delinked_stats$greater_than_95}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))
  
  ,
  
  sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 0.03, fill = "#685369") + 
  labs(x = "prior on group mean for pMem, post condition",
       title = "pMem group mean prior, inv_logit(alpha0_mu + alphaD_mu)") + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12))
  
  ,
  
  nrow = 1,
  align = "h"
)

##
## inv_logit(beta0_mu + betaD_mu) - inv_logit(beta0_mu) plot
##

betaD_mu_delinked_stats <- sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1) - exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  summarise(less_than_n80 = sum(delinked < -0.8)/n(), greater_than_80 = sum(delinked > 0.8)/n())

sim_datasets %>%
  transmute(delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1) - exp(beta0_mu)/(exp(beta0_mu) + 1)) %>%
  ggplot(aes(x = delinked)) + 
  geom_histogram(binwidth = 0.02, fill = "#00AEB2") + 
  geom_vline(xintercept = c(-0.8, 0.8), linetype = "dashed") + 
  labs(x = "prior on group mean for delta-pMem, mean post minus mean pre",
       title = "delta-pMem group mean prior, inv_logit(beta0_mu + betaD_mu) - inv_logit(beta0_mu)",
       subtitle = glue("prob(delta-pMem < -0.8) = {betaD_mu_delinked_stats$less_than_n80}\nprob(delta-pMem > 0.8) = {betaD_mu_delinked_stats$greater_than_80}")) + 
  theme(axis.title = element_text(size = 12),
        plot.title = element_text(size = 12)) + 
  scale_x_continuous(breaks= pretty_breaks(10))

* Notes

fairly standard prior on the pMem group mean, totally uninformative.

---

Prior predicitive distribution of pMem at the subject level

(based on simulated subjects from each dataset)

Marginal prior on subjects pre pMem, post pMem, and effect size

(ignoring simulation sample sizes)

sim_datasets_unnest <- sim_datasets %>%
  unnest(dataset) %>%
  mutate(beta0_mu_delinked = exp(beta0_mu)/(exp(beta0_mu) + 1),
         beta1_mu_delinked = exp(beta0_mu + betaD_mu)/(exp(beta0_mu + betaD_mu) + 1),
         subj_pre_pMem = exp(subj_beta0)/(exp(subj_beta0) + 1),
         subj_post_pMem = exp(subj_betaD + subj_beta0)/(exp(subj_betaD + subj_beta0) + 1),
         subj_pMem_ES = subj_post_pMem - subj_pre_pMem) 

pMem_ES_quantiles <- quantile(sim_datasets_unnest$subj_pMem_ES, c(0.025, 0.975))

plot_grid(
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(x = subj_pre_pMem)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.3) + 
  labs(x = "subj_pre_pMem [prior predictive distribution]",
       subtitle = glue("p(< 0.05) = {sum(sim_datasets_unnest$subj_pre_pMem < 0.05)/length(sim_datasets_unnest$subj_pre_pMem)}\n p(> 0.95) = {sum(sim_datasets_unnest$subj_pre_pMem > 0.95)/length(sim_datasets_unnest$subj_pre_pMem)}"))
  
  ,
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%  
  ggplot(aes(x = subj_post_pMem)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.3) + 
  labs(x = "subj_post_pMem [prior predictive distribution]",
       subtitle = glue("p(< 0.05) = {sum(sim_datasets_unnest$subj_post_pMem < 0.05)/length(sim_datasets_unnest$subj_post_pMem)}\n p(> 0.95) = {sum(sim_datasets_unnest$subj_post_pMem > 0.95)/length(sim_datasets_unnest$subj_post_pMem)}"))
  
  ,
  
  sim_datasets_unnest %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%  
  ggplot(aes(x = subj_pMem_ES)) + 
  geom_histogram(binwidth = 0.01, fill = "red", alpha = 0.7) + 
  geom_vline(xintercept = pMem_ES_quantiles, linetype = "dashed") + 
  labs(x = "subj_pMem_ES [prior predictive distribution], (5%, 95%) quantile lines",
       subtitle = glue("p(< -0.8) = {sum(sim_datasets_unnest$subj_pMem_ES < -0.8)/length(sim_datasets_unnest$subj_pMem_ES)}\n p(> 0.8) = {sum(sim_datasets_unnest$subj_pMem_ES > 0.80)/length(sim_datasets_unnest$subj_pMem_ES)}"))
  
  ,
  
  ncol = 1
)

Calculate min and max subject pre, post, and pMem effect size in each simulation.

sim_subj_extremes <- sim_datasets %>% 
  unnest(dataset) %>%
  mutate(subj_beta1 = subj_beta0 + subj_betaD, 
         subj_beta0_delinked = exp(subj_beta0)/(exp(subj_beta0) + 1), 
         subj_beta1_delinked = exp(subj_beta0 + subj_betaD)/(exp(subj_beta0 + subj_betaD) + 1), 
         subj_pMem_effect = subj_beta1_delinked - subj_beta0_delinked ) %>%
  group_by(sim_num) %>%
  summarize_at(vars(subj_beta0_delinked, subj_beta1_delinked, subj_pMem_effect), list(max = max, min = min)) 

Across-sim max pMem

plot_grid(

  #What is the max subject pre condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta0_delinked_max, fill = "red", alpha = 0.3), binwidth = 0.02) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: max subj pMem per sim [subj_beta0_delinked_max]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta0_delinked_max < 0.05)/length(sim_subj_extremes$subj_beta0_delinked_max)}\n p(> 0.95) = {sum(sim_subj_extremes$subj_beta0_delinked_max > 0.95)/length(sim_subj_extremes$subj_beta0_delinked_max)}"))
  
  ,

  #What is the max subject post condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta1_delinked_max, fill = "red", alpha = 0.3), binwidth = 0.02) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: max subj pMem per sim [subj_beta1_delinked_max]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta1_delinked_max < 0.05)/length(sim_subj_extremes$subj_beta1_delinked_max)}\n p(>0.95) = {sum(sim_subj_extremes$subj_beta1_delinked_max > 0.95)/length(sim_subj_extremes$subj_beta1_delinked_max)}"))

  ,
  ncol =1,
  align = 'v'

)

Across-sim min pMem

plot_grid(

  #What is the min subject pre condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta0_delinked_min, fill = "red", alpha = 0.3), binwidth = 0.02) +
  theme(legend.position = "none") + 
  labs(x = "pre condition: min subj pMem per sim [subj_beta0_delinked_min]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta0_delinked_min < 0.05)/length(sim_subj_extremes$subj_beta0_delinked_min)}\n p(> 0.95) = {sum(sim_subj_extremes$subj_beta0_delinked_min > 0.95)/length(sim_subj_extremes$subj_beta0_delinked_min)}"))
  
  ,

  #What is the min subject post condition value in each dataset
  sim_subj_extremes %>%
  ggplot() + 
  geom_histogram(aes(x = subj_beta1_delinked_min, fill = "red", alpha = 0.3), binwidth = 0.02) + 
  theme(legend.position = "none") + 
  labs(x = "post condition: min subj pMem per sim [subj_beta1_delinked_min]",
       subtitle = glue("p(< 0.05) = {sum(sim_subj_extremes$subj_beta1_delinked_min < 0.05)/length(sim_subj_extremes$subj_beta1_delinked_min)}\n p(>0.95) = {sum(sim_subj_extremes$subj_beta1_delinked_min > 0.95)/length(sim_subj_extremes$subj_beta1_delinked_min)}"))

  ,
  ncol =1,
  align = 'v'

)

Across-sim max+min pMem effect size

#What is the most extreme change from pre to post in a subject

min_plot <- sim_subj_extremes %>%
  mutate(subj_pMem_effect_min = if_else(subj_pMem_effect_min > 1 , 1, subj_pMem_effect_min)) %>%
  mutate(subj_pMem_effect_min = if_else(subj_pMem_effect_min < -1 , -1, subj_pMem_effect_min)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_pMem_effect_min, fill = "red", alpha = 0.3), binwidth = 0.03) +
  theme(legend.position = "none") + 
  labs(x = "min subj pMem effect per sim \n[min(subj_beta1_delinked - subj_beta0_delinked)]",
       subtitle = glue("p(<-0.8) = {sum(sim_subj_extremes$subj_pMem_effect_min < -0.8)/length(sim_subj_extremes$subj_pMem_effect_min)}\n p(>0.8) = {sum(sim_subj_extremes$subj_pMem_effect_min > 0.8)/length(sim_subj_extremes$subj_pMem_effect_min)}")) + 
  xlim(c(-1, 1))

#What is the most extreme subject post condition value in each dataset
max_plot <- sim_subj_extremes %>%
  mutate(subj_pMem_effect_max = if_else(subj_pMem_effect_max > 1 , 1, subj_pMem_effect_max)) %>%
  mutate(subj_pMem_effect_max = if_else(subj_pMem_effect_max < -1 , -1, subj_pMem_effect_max)) %>%
  ggplot() + 
  geom_histogram(aes(x = subj_pMem_effect_max, fill = "red", alpha = 0.3), binwidth = 0.03) +
  theme(legend.position = "none") + 
  labs(x = "max subj pMem effect per sim \n[max(subj_beta1_delinked - subj_beta0_delinked)]",
       subtitle = glue("p(<-0.8) = {sum(sim_subj_extremes$subj_pMem_effect_max < -0.8)/length(sim_subj_extremes$subj_pMem_effect_max)}\n p(>0.8) = {sum(sim_subj_extremes$subj_pMem_effect_max > 0.8)/length(sim_subj_extremes$subj_pMem_effect_max)}")) + 
    xlim(c(-1, 1))

plot_grid(min_plot, max_plot, ncol =1, align = 'v')

## Warning: Removed 2 rows containing missing values (geom_bar).

## Warning: Removed 2 rows containing missing values (geom_bar).

* Notes

prior predictive dists for pre, post and ES dont look bad. though, max + min plots could be less extreme.

---

Joint prior on pre condition + effect size

joint_pre_plot <- sim_datasets_unnest %>% 
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  ggplot(aes(y = exp(subj_alpha0), x = exp(subj_beta0)/(exp(subj_beta0) + 1))) +
    geom_point() +
    labs(x = 'pMem, pre', y = 'circSD, pre')

plot_grid(
  joint_pre_plot,
  ncol = 1,
  align = 'v'
)

joint_ES_plot <- sim_datasets_unnest %>% 
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  mutate(subj_pMem_ES = exp(subj_beta0 + subj_betaD)/(exp(subj_beta0 + subj_betaD) + 1) - exp(subj_beta0)/(exp(subj_beta0) + 1),
         subj_circSD_ES = exp(subj_alpha0 + subj_alphaD) - exp(subj_alpha0)) %>%
  ggplot(aes(x = subj_pMem_ES, y = subj_circSD_ES)) +
    geom_point() +
    geom_vline(xintercept = 0, linetype = 'dashed') + 
    geom_hline(yintercept = 0, linetype = 'dashed')
  
plot_grid(
  joint_ES_plot,
  joint_ES_plot + ylim(c(-200, 200)) + labs(subtitle = "zoom in"),
  ncol = 1,
  align = 'v'
)

## Warning: Removed 79 rows containing missing values (geom_point).

---

Prior predicitive distribution at the observation level, per condition

(based on simulated obs from each dataset, ignoring subject labels)

#######################################################
# calculate histogram quantile mats from each condition

sim_subj_obs_hist_count <- function(dataset, condition = 0){
  
  dataset_obs <- dataset %>% 
    sample_n(1) %>%
    unnest(subj_obs) %>%
    filter(stimulation == condition) %>%
    select(obs_degree)
  
  breaks <- seq(-180, 180, 5)
  
  bincount <- hist(dataset_obs$obs_degree, breaks = breaks, plot = FALSE)$counts
  
  bincount_names <- glue("c{breaks[-1]}")
  
  names(bincount) <- bincount_names
  bincount_df <- data.frame(as.list(bincount))

  return(bincount_df)
  
}

make_quantmat <- function(sim_datasets, condition = 0){

  bincounts <- sim_datasets %>% 
  select(dataset) %>% 
  mutate(subj_hist_counts = map(dataset, sim_subj_obs_hist_count, condition)) %>% 
  select(-dataset) %>% 
  unnest(subj_hist_counts) %>%
  as_tibble()


  xvals <- seq(-177.5, 177.5, 5)
  probs <- seq(0.1,0.9,0.1)

  quantmat <- as.data.frame(matrix(NA, nrow=ncol(bincounts), ncol=length(probs)))
  names(quantmat) <- paste0("p",probs)

  quantmat <- cbind(quantmat, xvals)

  for (iQuant in 1:length(probs)){
   quantmat[,paste0("p",probs[iQuant])] <- as.numeric(summarise_all(bincounts, ~quantile(., probs[iQuant])))
  }
    
  return(quantmat)
}

quantmat_cond0 <- make_quantmat(sim_datasets, 0)
quantmat_cond1 <- make_quantmat(sim_datasets, 1)


#######################################################
# calculate ecdf quantile mats from each condition

# unnest sim_datasets, using only 1 subj/dataset
unnested <- 
  sim_datasets %>%
  unnest(dataset) %>%
  group_by(sim_num) %>%
  sample_n(1) %>%
  ungroup() %>%
  unnest(subj_obs)

# calc quantiles mat for pre condition
ecdf_res_stim0 <- 
  unnested %>% 
  filter(stimulation == 0) %>%
  group_by(sim_num) %>% 
  group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))

stim0_ecdf_quantiles <- bind_cols(
  tibble(x_val = seq(-180, 180, 1)), 
  as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim0), probs = c(0.95, 0.5, 0.05 )))
  )

# calc quantiles mat for post condition
ecdf_res_stim1 <- 
  unnested %>% 
  filter(stimulation == 1) %>%
  group_by(sim_num) %>% 
  group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))

stim1_ecdf_quantiles <- bind_cols(
  tibble(x_val = seq(-180, 180, 1)), 
  as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim1), probs = c(0.95, 0.5, 0.05 )))
  )

# blues
b_light <- "#8C9BC4"
b_light_highlight <- "#A0ADCE"
b_mid   <- "#546BA9"
b_mid_highlight   <- "#7385B8"
b_dark  <- "#002381"
b_dark_highlight  <- "#2E4B97"

#betancourt reds
r_light <- "#DCBCBC"
r_light_highlight <- "#C79999"
r_mid   <- "#B97C7C"
r_mid_highlight   <- "#A25050"
r_dark  <- "#8F2727"
r_dark_highlight  <- "#7C0000"


#######################################################
# plot histogram(density) per condition

ggplot(quantmat_cond0, aes(x = xvals)) + 
  geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = r_light, alpha = 0.4) + 
  geom_line(aes(y = p0.5), color = r_dark, size = 1) + 
  geom_ribbon(data = quantmat_cond1, aes(ymax = p0.9, ymin = p0.1), fill = b_light, alpha = 0.4) + 
  geom_line(data = quantmat_cond1, aes(y = p0.5), color = b_dark, size = 1) + 
  scale_x_continuous(breaks=pretty_breaks(10)) + 
  labs(x = "error (degrees) [red = pre, blue = post]", 
       y = "count +/- quantile", 
       subtitle = glue("per-condition prior pred dist (median line, 90% interval over {nrow(sim_datasets)} sim datasets)\n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw)")) + 
  theme_cowplot()

#######################################################
# plot ecdf per condition

ggplot() +
  geom_ribbon(data = stim0_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "red", alpha = 0.3) + 
  geom_line(data = stim0_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "red", size = 1) +
  geom_ribbon(data = stim1_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "blue", alpha = 0.3) + 
  geom_line(data = stim1_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "blue", size = 1) + 
  scale_x_continuous(breaks=pretty_breaks(10)) + 
  geom_hline(yintercept = seq(0, 1, 0.25), linetype = "dashed", alpha = 0.2) +
  labs(x = "error (degrees) [red = pre, blue = post]", 
       y = "cumulative prob.", 
       subtitle = glue("per-condition prior pred cdf (median line, 90% interval over {nrow(sim_datasets)} sim datasets) \n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw"))

plot_grid(          
                                                                  
  ggplot(quantmat_cond0, aes(x = xvals)) + 
    geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = c_light) + 
    geom_ribbon(aes(ymax = p0.8, ymin = p0.2), fill = c_light_highlight) + 
    geom_ribbon(aes(ymax = p0.7, ymin = p0.3), fill = c_mid) + 
    geom_ribbon(aes(ymax = p0.6, ymin = p0.4), fill = c_mid_highlight) + 
    geom_line(aes(y = p0.5), color = c_dark, size = 1) + 
    scale_x_continuous(breaks=pretty_breaks(10)) + 
    coord_cartesian(ylim = c(0, 150)) + 
    labs(x = "error (degrees)", y = "count +/- quantile", subtitle = "without stimulation")
  ,

  ggplot(quantmat_cond1, aes(x = xvals)) + 
    geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = c_light) + 
    geom_ribbon(aes(ymax = p0.8, ymin = p0.2), fill = c_light_highlight) + 
    geom_ribbon(aes(ymax = p0.7, ymin = p0.3), fill = c_mid) + 
    geom_ribbon(aes(ymax = p0.6, ymin = p0.4), fill = c_mid_highlight) + 
    geom_line(aes(y = p0.5), color = c_dark, size = 1) + 
    scale_x_continuous(breaks=pretty_breaks(10)) +
    coord_cartesian(ylim = c(0, 150)) + 
    labs(x = "error (degrees)", y = "count +/- quantile", subtitle = "with stimulation")
  ,
  
  sim_datasets %>%
    sample_n(1) %>%
    unnest(dataset) %>%
    unnest(subj_obs) %>% 
    filter(stimulation == sample(c(0,1), 1)) %T>%
    print() %>%
    ggplot(aes(x = obs_degree)) + 
    geom_density() + 
    labs(subtitle = "correctness check: random simulation, random condition") + 
    scale_x_continuous(breaks=pretty_breaks(10))
  ,
  
  ncol = 1,
  align = "v"
)

* Notes

no much gleaned from these prior plots, except that the prior expects no effect and the post condition has larger variance of probability.